Find the Degree, Leading Term, and Leading Coefficient (3x^5-2)(9x+4)

$(3 x^{5} - 2) (9 x + 4)$

Simplify the polynomial, then reorder it left to right starting with the highest degree term.

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Expand $(3 x^{5} - 2) (9 x + 4)$ using the FOIL Method.

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Apply the distributive property.

$3 x^{5} (9 x + 4) - 2 (9 x + 4)$

Apply the distributive property.

$3 x^{5} (9 x) + 3 x^{5} \cdot 4 - 2 (9 x + 4)$

Apply the distributive property.

$3 x^{5} (9 x) + 3 x^{5} \cdot 4 - 2 (9 x) - 2 \cdot 4$

Simplify each term.

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Rewrite using the commutative property of multiplication.

$3 \cdot 9 (x^{5} x) + 3 x^{5} \cdot 4 - 2 (9 x) - 2 \cdot 4$

Multiply $x^{5}$ by $x$ by adding the exponents.

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Multiply $x^{5}$ by $x$ .

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Raise $x$ to the power of $1$ .

$3 \cdot 9 (x^{5} x^{1}) + 3 x^{5} \cdot 4 - 2 (9 x) - 2 \cdot 4$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$3 \cdot 9 x^{5 + 1} + 3 x^{5} \cdot 4 - 2 (9 x) - 2 \cdot 4$

Add $5$ and $1$ .

$3 \cdot 9 x^{6} + 3 x^{5} \cdot 4 - 2 (9 x) - 2 \cdot 4$

Multiply $3$ by $9$ .

$27 x^{6} + 3 x^{5} \cdot 4 - 2 (9 x) - 2 \cdot 4$

Multiply $4$ by $3$ .

$27 x^{6} + 12 x^{5} - 2 (9 x) - 2 \cdot 4$

Multiply $9$ by $- 2$ .

$27 x^{6} + 12 x^{5} - 18 x - 2 \cdot 4$

Multiply $- 2$ by $4$ .

$27 x^{6} + 12 x^{5} - 18 x - 8$

The degree of a polynomial is the highest degree of its terms.

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Identify the exponents on the variables in each term, and add them together to find the degree of each term.

$27 x^{6} \to 6$

$12 x^{5} \to 5$

$- 18 x \to 1$

$- 8 \to 0$

The largest exponent is the degree of the polynomial.

$6$

The leading term in a polynomial is the term with the highest degree.

$27 x^{6}$

The leading coefficient of a polynomial is the coefficient of the leading term.

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The leading term in a polynomial is the term with the highest degree.

$27 x^{6}$

The leading coefficient in a polynomial is the coefficient of the leading term.

$27$

List the results.

Polynomial Degree: $6$

Leading Term: $27 x^{6}$

Leading Coefficient: $27$

Find the Degree, Leading Term, and Leading Coefficient (3x^5-2)(9x+4)